Search for dissertations about: "pluripotential theory"
Showing result 1 - 5 of 7 swedish dissertations containing the words pluripotential theory.
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1. Dirichlet's problem in Pluripotential Theory
Abstract : In this thesis we focus on Dirichlet's problem for the complex Monge-Ampère equation. That is, for a given non-negative Radon measure µ we are interested in the conditions under which there exists a plurisubharmonic function u such that (ddcu)n=µ, where (ddc)n is the complex Monge-Ampère operator. READ MORE
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2. The complex Monge-Ampére operator on bounded hyperconvex domains
Abstract : .... READ MORE
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3. Boundary singularities of plurisubharmonic functions
Abstract : We study the Perron–Bremermann envelope P(μ, φ):=sup{u(z) ; u ∈ PSH(Ω), (ddcu)n≥ μ, u^* ≤ φ} on a B-regular domain Ω. Such envelopes occupy a central position within pluripotential theory as they, for suitable μ and φ harmonic and continuous on the closure of Ω, constitute unique solutions to the Dirichlet problem for the complex Monge–Ampère operator. READ MORE
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4. Multipoint Okounkov bodies, strong topology of ω-plurisubharmonic functions and Kähler-Einstein metrics with prescribed singularities
Abstract : The most classical topic in Kähler Geometry is the study of Kähler-Einstein metrics as solution of complex Monge-Ampère equations. This thesis principally regards the investigation of a strong topology for ω-plurisubharmonic functions on a fixed compact Kähler manifold (X,ω), its connection with complex Monge-Ampère equations with prescribed singularities and the consequent study of singular Kähler-Einstein metrics. READ MORE
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5. Pluripotential-theoretic methods in K-stability and the space of Kähler metrics
Abstract : It is a natural problem, dating back to Calabi, to find canonical metrics on complex manifolds. In the case of polarized compact Kähler manifolds, a natural candidate is a metric with constant scalar curvature (cscK metric). READ MORE